Simplify the following expression: $\dfrac{36x^3}{3x^4}$ You can assume $x \neq 0$.
Solution: $ \dfrac{36x^3}{3x^4} = \dfrac{36}{3} \cdot \dfrac{x^3}{x^4} $ To simplify $\frac{36}{3}$ , find the greatest common factor (GCD) of $36$ and $3$ $36 = 2 \cdot 2 \cdot 3 \cdot 3$ $3 = 3$ $ \mbox{GCD}(36, 3) = 3 $ $ \dfrac{36}{3} \cdot \dfrac{x^3}{x^4} = \dfrac{3 \cdot 12}{3 \cdot 1} \cdot \dfrac{x^3}{x^4} $ $\phantom{ \dfrac{36}{3} \cdot \dfrac{3}{4}} = 12 \cdot \dfrac{x^3}{x^4} $ $ \dfrac{x^3}{x^4} = \dfrac{x \cdot x \cdot x}{x \cdot x \cdot x \cdot x} = \dfrac{1}{x} $ $ 12 \cdot \dfrac{1}{x} = \dfrac{12}{x} $